How Much Rosin is Enough?
The amount of rosin applied to the bow and how often you apply it can drastically affect the sound produced when you play. The purpose of the rosin is to help the hairs on the bow grab the string as it is drawn across, and to cause the string to vibrate, thereby producing the sound. In the early beginner stage, it is hard to know when you need more rosin, but as your technique develops, it will become very easy to tell when more is necessary. To apply rosin to the hair, tighten the bow as normal for playing, hold the rosin in the left hand and slide the hair on the rosin all the way from the frog to the tip and back, pushing the bow somewhat firmly into the rosin. Scratching the surface of brand new rosin with a key helps the rosin come off easier on the hair, so you can do that to make the process faster.
When a bow is used for the first time and there has never been rosin applied, the hairs will slip across the string without producing sound at all. You will need to put a lot of rosin on a new bow. Do 20 strokes back and forth, then test it on the string. Do another 20 and try again, until it seems like the right amount. When a student gets a new bow, I always encourage them to play a little bit without any rosin, just to feel how the bow slides across the string without resistance. That helps in understanding the feeling of not having enough rosin.
Not Enough Rosin
If your bow seems to be slipping across the string, not grabbing the string as you draw it across, or not producing an even, solid tone, you may need to apply more rosin. Usually the sound is weak, inconsistent, and airy. Some bows have hair that does not hold rosin well, or may need to be re-haired. With this type of bow, you can keep applying more rosin but still the bow makes a weak sound or slips across the string. Occasionally, lower quality bows will have hair that after a few months of use will not hold rosin at all. Normally, these bows need to be replaced completely, as a re-hairing may cost as much as replacing the bow.
Too Much Rosin
If there is too much rosin on the hair, the bow will feel sticky on the string, resist moving across the string smoothly, and will result in an uneven sound. You may also notice a cloud of dust coming off the hair, and sticky powder from the excess rosin collecting on the strings, landing on the surface of the instrument near the bridge and on the fingerboard.
The Right Amount
On average, you should apply a few (about 5) strokes of rosin before each practice session or performance. If you are practicing frequently or for many hours in a day you will find that you need more rosin more often. If you are not practicing much, you will go longer before more rosin is needed. If you are in doubt whether you need more rosin, then you should put some more rosin on the bow. If there is too much, the problem is easily handled by wiping the excess away, but students who routinely play with too little rosin learn bad bowing habits because they are playing with an unnecessary hardship they are not aware of. With too little rosin, the tendency is to squeeze the bow and push it harder than necessary into the string which can cause big problems with bowing in the long run.
Accumulation of rosin dust happens even with proper rosining practices, and it is important to always lightly wipe off excess rosin dust after each practice session. Keep a soft, lint-free cloth handy in your case for cleaning. My younger students often drop and break their rosin, resulting in a few larger pieces and many small ones. I advise them to keep the biggest part and throw the rest away. You can use the big piece for a long, long time, so you usually don't have to buy new rosin.